Computational Statistics

, Volume 32, Issue 2, pp 409–428 | Cite as

Unsupervised learning of pharmacokinetic responses

  • Elson Tomás
  • Susana Vinga
  • Alexandra M. CarvalhoEmail author
Original Paper


Pharmacokinetics (PK) is a branch of pharmacology dedicated to the study of the time course of drug concentrations, from absorption to excretion from the body. PK dynamic models are often based on homogeneous, multi-compartment assumptions, which allow to identify the PK parameters and further predict the time evolution of drug concentration for a given subject. One key characteristic of these time series is their high variability among patients, which may hamper their correct stratification. In the present work, we address this variability by estimating the PK parameters and simultaneously clustering the corresponding subjects using the time series. We propose an expectation maximization algorithm that clusters subjects based on their PK drug responses, in an unsupervised way, collapsing clusters that are closer than a given threshold. Experimental results show that the proposed algorithm converges fast and leads to meaningful results in synthetic and real scenarios.


Clustering Expectation-maximization One-compartment model 



The authors would like to express their appreciation to Paulo Mateus for many useful inputs and valuable comments. Special thanks go to the anonymous reviewers, who significant contributed to the quality of this manuscript with their valuable and well-aimed comments. This work was supported by national funds through FCT, Fundação para a Ciência e a Tecnologia, under contracts LAETA (UID/EMS/50022/2013) and IT (UID/EEA/50008/2013), and by projects InteleGen (PTDC/DTP-FTO/1747/2012), PERSEIDS (PTDC/EMS-SIS/0642/2014) and internal IT project QBigData. SV acknowledges support by Program Investigador FCT (IF/00653/2012) from FCT, co-funded by the European Social Fund (ESF) through the Operational Program Human Potential (POPH). This work was partially supported by the European Union’s Horizon 2020 research and innovation program under grant agreement No. 633974 (SOUND project).


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Elson Tomás
    • 1
  • Susana Vinga
    • 1
  • Alexandra M. Carvalho
    • 2
    Email author
  1. 1.IDMEC, Instituto Superior TécnicoUniversidade de LisboaLisbonPortugal
  2. 2.Instituto de Telecomunicações, Instituto Superior TécnicoUniversidade de LisboaLisbonPortugal

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